AI 中文总结
该研究构建自洽双流体晕模型，计算暗物质混合中子星的弱引力偏折，发现其偏折与点质量预测有明显差异，可用于解决暗物质与核态方程的简并性问题。
AI 中文摘要
我们计算了携带自洽暗物质组分的中子星对光的弱引力偏折，该暗物质形成延伸至重子表面之外的“扩展晕”。该构型的提出源于两项观测：其一，局限在重子半径内的暗物质核心不会留下独特的透镜信号，因为根据伯克霍夫定理，外部是具有总质量的史瓦西时空，因此经过恒星外部的光线仅会感受到该总质量及其对应的致密性；其二，我们所寻求的信号存在于互补情形中，即光线确实穿过晕，使得周围密度直接进入光学几何结构。我们通过耦合双流体托尔曼-奥本海默-沃尔科夫方程对恒星进行建模，其中重子与暗组分仅通过引力相互作用，并通过高斯-博内定理的吉本斯-维尔纳构造从所得外部轮廓获得偏转角。该方法的核心特征是，偏折与“自洽”双流体轮廓相关，而非人为插入的介质。我们表明，对于小于晕半径的碰撞参数，偏折会明显偏离点质量预测，该亏缺由暗物质占比和晕范围决定，且我们认为该亏缺的“形状”提供了一种基于几何透镜的方法，用于解决暗物质与核态方程之间的简并性问题。该框架因此将致密星的结构建模与其引力透镜现象学统一起来。
英文摘要
We compute the weak gravitational deflection of light by a neutron star that carries a self-consistent dark-matter component, in the regime in which the dark matter forms an "extended halo" reaching beyond the baryonic surface. Two observations motivate this configuration. First, a dark-matter core confined within the baryonic radius leaves no distinctive lensing signature, since by Birkhoff's theorem the exterior is Schwarzschild with the total mass, so a ray passing outside the star feels only that mass and the compactness it implies. Second, the signature we seek resides in the complementary case, in which the ray genuinely traverses the halo, so that the surrounding density enters the optical geometry directly. We model the star by integrating the coupled two-fluid Tolman--Oppenheimer--Volkoff equations, with the baryonic and dark components interacting solely through gravity, and we obtain the deflection angle from the resulting external profile through the Gibbons--Werner construction of the Gauss--Bonnet theorem. The defining feature of the approach is that the deflection is tied to a "self-consistent" two-fluid profile rather than to a medium inserted by hand. We show that, for impact parameters smaller than the halo radius, the deflection departs measurably from the point-mass prediction, the deficit being governed by the dark-matter fraction and the halo extent, and we argue that the "shape" of this deficit furnishes a geometric, lensing-based handle on the degeneracy between dark matter and the nuclear equation of state. The framework thereby unites the structural modelling of compact stars with their gravitational-lensing phenomenology.
Comments10 pages, 5 figures
